Talks

Abstract: In this talk, I'll first discuss simple stochastic processes that are subject to a global constraint, e.g., a single Brownian bridge. An important algorithmic issue is how to numerically generate such globally constrained configurations via a rejection-free method. I will illustrate how this can be done by writing an effective, but exact Langevin equation. I will then generalise this idea of effective Langevin equation to interacting particles, with global as well as local dynamical constraints, with the example of nonintersecting Brownian bridges. A deep connection to random matrix theory and matrix models will be elucidated.

Abstract: The winding number is a concept in complex analysis which has, in the presence of chiral symmetry, a physics interpretation as the topological index belonging to gapped phases of fermions. We study statistical properties of this Topological quantity. To this end, we set up a random matrix model for a chiral unitary system with a parametric dependence. We analytically calculate the discrete Probability distribution of the winding numbers, as well as the parametric correlations functions of the winding number density. Moreover, we address aspects of universality for the two-point function of the winding number density by identifying a proper unfolding procedure. We conjecture the unfolded two-point function to be universal.

Abstract: Quantum circuits built from dual-unitary gates offer a range of dynamical possibilities from the integrable to the maximally chaotic many-body systems. We will discuss the effect of random onsite operators on such circuits which leads to the study of spectral gaps in maps which determine the decay of correlations. We find that the entangling power of the unitary gates play a central role in these random circuits, with the average spectral gap being a universal function of it.

Abstract: Linking thermodynamic variables like temperature $T$ and the measure of chaos, the Lyapunov exponents $\lambda$, is a question of fundamental importance in many-body systems. By using nonlinear fluid equations in one and three dimensions, we show that in thermalised flows $\lambda \propto \sqrt{T}$, in agreement with results from frustrated spin systems. This suggests an underlying universality and provides evidence for recent conjectures on the thermal scaling of $\lambda$. We also reconcile seemingly disparate effects---equilibration on one hand and pushing systems out-of-equilibrium on the other---of many-body chaos by relating $\lambda$ to $T$ through the dynamical structures of the flow.

Abstract: Since a rigorous microscopic treatment of a nematic fluid system based on a pairwise interaction potential is immensely complex, we had introduced a simple mean field potential to take into account the various aspects of a smectic A–nematic phase transition. In particular, we have studied the dependence of the phase transition on the coupling coefficient between the nematic and smectic order parameters, which in turn depends on the length of alkyl chain, variation of density, entropy, and specific heat. Detailed investigation on the coupling parameter shows the existence of a smectic A–nematic–isotropic triple point as well as a tricritical point where the smectic–nematic phase transition changes its nature from the second to the first order. It is also seen that the application of pressure can result in the appearance of a nematic phase. Based on these findings, we believe that by varying the two model parameters which appeared in our calculation, many different liquid crystalline materials can also be studied.

Abstract: The Widom-Rowlinson lattice gas is a two-species (A/B) model with prohibition of A-B nearest-

neighbor pairs; it exhibits phase separation above a critical density. Under a drive, remarkable

properties emerge, such as lamellar ordering perpendicular to the drive, and kink singularities in the structure factor [1]. The preferred wavelength of the stripe pattern varies with density and drive strength. As we increase the system size at fixed drive and density, a sequence of transitions from n to n+1 stripes occurs. Even below the critical density, we observe (damped) oscillations in spatial composition correlations. I will briefly mention ongoing efforts to develop a continuous, stochastic description of the model [2].

[1] R. Dickman and R.K.P. Zia, Phys Rev. E 97, 062126 (2018).

[2] M. O. Lavrentovich, R. Dickman, and R.K.P. Zia, Phys Rev. E 104, 064135 (2021).

Abstract: Liquids are known to have homogeneous structure and dynamics. However, in the supercooled liquid regime, the dynamics is heterogenous and this heterogeneity increases with a decrease in temperature. The origin of this dynamic heterogeneity is a topic of intense research. In analogy with crystals where under external perturbation regions with structural defects show a higher probability of rearrangements, it is often suggested that in supercooled liquids such structural defects may also be present, giving rise to the dynamic heterogeneity. However, while identifying structural defects in crystals with otherwise well-defined structure is trivial, doing the same in a supercooled liquid where particles are arranged in a disordered manner is a nontrivial task. In this talk, I will first show that we can describe the local structure in terms of a local caging potential and its softness using dynamic density functional theory. This microscopic softness can capture the structural heterogeneity, and the lifetime of the softness parameter is similar to the lifetime of the cage. Finally, I will show that our theory predicts that the local softness and the local dynamics are causal. With the decrease in temperature, the correlation between structure and dynamics increases. The study shows that at lower temperatures, the structural heterogeneity increases, and since the structure becomes a better predictor of the dynamics, it leads to an increase in the dynamical heterogeneity.

Abstract: A binary mixture with large size ratio shows a timescale separation of relaxation processes among the constituents. In such a

mixture, bigger species may show glass transition around the critical density of mode-coupling theory and smaller species remain mobile with a relatively weak decrease of their selfdiffusion coefficient with increasing density. We use large-scale molecular dynamics simulations with a model bidisperse colloidal soft-spheres mixture to show how finite-size effects can be understood in such mixtures from the analysis of the collective interdiffusion dynamics. Further, we study the response of the mixture to external shear, across a wide range of densities. The system shows complex macro rheological response, and we try to understand these observations by probing the microscopic structural and dynamical properties of the system. We demonstrate that the interplay of the time scales associated with applied shear and the intrinsic relaxation of the species leads to the observed density-dependent response.

References:

1. V. Vaibhav, J. Horbach, and P. Chaudhuri; Rheological response of a glass-forming liquid having large bidispersity; arXiv:2202.12612

2. V. Vaibhav, J. Horbach, and P. Chaudhuri; Finite-size effects in the diffusion dynamics of a glass-forming binary mixture with large

size ratio; arXiv:2202.12189

Abstract: Recent computational investigations of yielding in amorphous solids under cyclic shear reveal striking dependence on annealing, similarly to yielding under uniform shear, and intriguing relaxation behaviour that are not fully understood. Striking differences are observed when deformation is applied asymmetrically to the initial state, rather

than symmetrically. Recently proposed schematic models for yielding are described, which capture key features of the yielding behaviour both for symmetric and asymmetric cyclic shear. Investigation of these models also lead to an appealing approach to understanding fatigue failure.

Abstract: Diversity in the natural world emerges from the collective behavior of large numbers of interacting objects. Statistical physics provides the framework relating microscopic to macroscopic properties. A fundamental assumption underlying this approach is that we have complete knowledge of the interactions between the microscopic entities. But what if that, even though possible in principle, becomes impossible in practice ? Can we still construct a framework for describing their collective behavior ? Dense suspensions and granular materials are two often quoted examples where we face this challenge. These are systems where because of the complicated surface properties of particles there is extreme sensitivity of the interactions to particle positions. In this talk, I will present a perspective based on notions of constraint satisfaction that provides a way forward. I will focus on our recent work on the emergence of elasticity in the absence of any broken symmetry, and sketch out other problems that can be addressed using this perspective.

Abstract: All solids flow at high enough applied stress and melt at high enough temperature. Crystalline solids flow and premelt via localized particle rearrangements that occur preferentially at structural defects known as dislocations. The population of dislocations therefore controls both how crystalline solids flow and how they melt. In glassy systems we have used machine learning to define a particle-based quantity, “softness,” that is highly correlated with the propensity of the particle to rearrange. I will describe how we use softness to build theories for dynamical phenomena in glassy liquids and plasticity in quasistatically-sheared athermal jammed packings.

Abstract: I will discuss some non-Markovian random walks as paradigms of stochastic processes with memory. In particular, I will demonstrate how such a statistical mechanics framework can be used to model repeated decision-making with distorted human recall of past experiences. In the case of two choices with different utility distributions, it is possible for an agent to become "trapped" in one of the choices on the basis of their early experiences. Significantly, it turns out that, under certain conditions, there is a optimal level of noise in the decision process which maximizes the expected returns in the long run.

[Based partly on Physica A 593, 126762 (2022), joint work with Evangelos Mitsokapas]

Abstract: I will discuss measurements of the low frequency resistance noise in strongly correlated oxides (e.g. V2O3 and NdNiO3) undergoing an abrupt Mott transition [1,2]. We have observed attributes of criticality—slowing down of order parameter fluctuations

accompanied by their enhanced variance (`critical opalescence’)—in these systems which have a strong abrupt transition accompanied by a pronounced hysteresis. These features suggest that the abrupt transition is controlled by a critical-like singularity in the hysteretic metastable phase. The singularities are identified with the spinodal points. Their observation is the likely consequence of the effectiveness of long-ranged nature of the elastic forces in suppressing thermodynamic fluctuations.

References

1. S. Kundu, T. Bar, R. K. Nayak, and B. Bansal, Phys. Rev. Lett. 124, 095703 (2020).

2. T. Bar, S. K. Choudhary, Md. A. Ashraf, K. S. Sujith, S. Puri, S. Raj, and B. Bansal, Phys. Rev. Lett. 121, 045701 (2018).

Abstract: Over the recent years there has a lot of interest, from experimental, numerical, and theoretical sides, to elucidate the hydrodynamic scale of integrable many-body systems. To explain the underlying microscopic structure I will use the classical Toda lattice as convenient model system. A comparison between theoretical predictions and molecular dynamics simulations will be discussed.

Abstract: The rate of entropy production provides a useful quantitative measure of how far a system is from equilibrium and estimating it directly from time-series data from experiments is desirable. Several approaches have been considered for stationary as well as non-stationary dynamics, some of which are based on a variational characterization of the entropy production rate. These latter usually however only give bounds and not the exact value. In earlier work, we have shown that a variational scheme based on the finite-time thermodynamic uncertainty relation can be modified (by considering short time series) and by this means give the exact value of the entropy production rate, and not just a bound.

In this talk, I will talk about this result and some of its implications and extensions.

Abstract: In this talk, I will present a personal perspective on the theory of self-organized criticality, mainly based on my own work. How
much of the bold vision presented in Bak Tang Wiesenfeld’s seminal paper of 1987 has been achieved? What are the lessons learnt ? What are the challenges ahead?

Abstract: We will survey the scenario of Floquet Quantum Matter, focussing especially on the question of its stability in presence of interactions without disorder. Such a stability is considered antithetical to common intuitions of ergodicity in a driven system. We will analyze the results through the lenses of series expansions and their startling asymptotic behaviours.

Abstract: We characterise the energy transport in a one-dimensional Z3 chiral clock model. The model generalises the Z2 symmetric transverse field Ising model (TFIM). The model is parameterised by a chirality parameter θ, in addition to f and J which are analogous to the transverse field and the nearest neighbour spin coupling in the TFIM. Unlike the well studied TFIM and XYZ models, this cannot be transformed into a fermionic system. We use a matrix product states implementation of the Lindblad master equation to obtain the non-equilibrium steady state (NESS) in systems of sizes up to 48. We present the estimated NESS current and its scaling exponent gamma with respect to system size as a function of θ at different f/J. The estimated gamma(f/J,θ) point to a ballistic energy transport along a line of integrable points f=Jcos3θ in the parameter space; all other points deviate from ballistic transport and indicate super-diffusive or diffusive behaviour within the range of system sizes accessible. We also present results for quench dynamics in the system showing peculiar effects of chirality resulting in slow thermalisation at the edge of the system.

Abstract: In this talk I will discuss how one can perturbatively construct the local integral of motion (LIOM) of a spin in a large magnetic field coupled to an infinite system (bath). I will show that this construction can be expressed through the nested commutators of the spin-bath interaction and the bath Hamiltonian. Convergence of this construction depends on the asymptotic behavior of the Krylov coefficients. In particular, in generic chaotic systems this construction is asymptotic. I will show that the short time decay rate of the slowest operator is proportional to the square root of the long time decay rate set by the Fermi-Golden-Rule rate. One of the consequences of this construction is that LIOMs are asymptotically unstable in interacting disordered systems indicating instability of many body localization in the thermodynamic limit. This construction agrees very well with both recent and prior numerical results.

Abstract: Thermally activated barrier crossing is of central importance to understand many physical, chemical, and biological processes. Opposed to memory-free, i.e., viscous solvents, where this process is well understood, only little is known in case of non-Markovian baths. In a combined experimental and numerical study, we demonstrate that the hopping dynamics of a

Brownian particle in a viscoelastic bath is governed by two (instead of a single) time scales, which can differ by more than two orders of magnitude. Remarkably, only the larger one exhibits a barrier height-dependence while the shorter is rather constant. The short time scale, which is here experimentally observed for the first time, results from the exchange of elastic energy between the hopping particle and the bath which eventually facilitates barrier crossing. Our results are in excellent agreement with a simple two-particle model which provides a microscopic picture of the underlying processes[1].

[1] Ginot, Caspers, Krüger, Bechinger, Phys. Rev. Lett. 128, 028001 (2022)

Abstract: Active particle motion is different from Brownian motion of a passive particle. Such particles perform self propulsion by transducing the available energy to systematic motion and thus break detailed balance. It is expected for them to exhibit interesting phenomena dissimilar to those shown by passive particles. While it is already known that at the collective level they display exotic phenomena, at the microscopic level also one observes interesting features. In this talk I will describe some of our recent results concerning the motion of active particles at microscopic level, which in some cases involve interesting crossover and universal features.

Abstract: Active matter is made of a large number of out of equilibrium interacting units, which convert some source of energy into directed motion. In contrast with systems driven out of equilibrium by an external field, or through the boundaries, the departure from equilibrium is local and independent for each active unit. Not so surprisingly, active matter exhibits rich collective phenomena at large scales, such as new types of phase separation and/or collective directed motion. The past 25 years have seen a surge of experimental observations and theoretical progress in the description of such phenomena in the realm of active liquids.

There are however a number of circumstances under which the description in terms of liquids is not suited. One can think of ants building solid bridges out of their bodies, meta-materials made of mechanically connected engines, cohesive cell layers or simply very dense assemblies of self-propelled particles forming a glass or a crystal. In such cases a description in terms of elastic solid is likely to be more appropriate. However very little is known about the actuation of an elastic lattice by polar active particles, the orientations of which may couple to the displacement field.

In this talk, I will present very recent experimental and theoretical works aiming at developing this new path of research in active matter. Doing so, we shall unveil two new types of collective phenomena : spontaneous flows in active crystals and collective actuation. We will specifically discuss how the coupling between linear elasticity and activity leads to a rich selection mechanism of the actuated dynamics.

Abstract: Active Brownian heat engines is one of the popular topics among researchers. These machines in contact with a heat reservoir consisting of active particles rectify energy into work. These "active" systems are inherently non-equilibrium. In such a scenario, the energy currents in the system can be termed as thermodynamic heat only if an effective equilibrium description can be given to it. We will discuss some general results to show under which conditions such a mapping is possible. In this context, we will also discuss a few specific models that are widely used to model active fluctuations.

Abstract: Transport phenomenon and active matter are two very important and popular fields in nonequilibrium statistical physics. In this work, we try to address a question at the juncture of these two fields, namely, how the transport properties of an extended Hamiltonian

system are affected when connected to active reservoirs. We study the energy transport between two active reservoirs connected by a chain of harmonic oscillators. We find that the stationary active current (i) changes non-monotonically as the activity of the reservoirs are changed, leading to a negative differential conductivity (NDC), and (ii) exhibits an unexpected direction reversal at some finite value of the activity drive. The origin of this NDC is traced back to the Lorentzian frequency spectrum of the active reservoirs. We provide another

physical insight to the NDC using nonequilibrium linear response formalism for the example of a dichotomous active force. We also show that despite an apparent similarity of the kinetic temperature profile to the thermally driven scenario, no effective thermal picture can be consistently built in general. However, such a picture emerges in the small activity limit, where many of the well-known results are recovered.

Abstract: Optimal control is essential for developing high-performing quantum machines. However, devising such control protocols can be highly non-trivial for many-body systems, owing to the exponentially diverging dimensions of the associated Hilbert spaces. I will talk about optimal control in many-body quantum critical batteries; I will discuss how one can use Kibble-Zurek mechanism to develop optimal control protocols even for quantum batteries modeled with many-body non-integrable systems.

Abstract: I will show how the melting of an interface in the 2D Ising model in transverse and longitudinal field shows signs of localization and, in the presence of disorder, of many-body scars. This is done by means of a mapping to a 1D model of fermions in the large ferromagnetic coupling J limit and after the systematic introduction of 1/J corrections.

Abstract: Lattice gauge theories (LGT) play a fundamental role both in condensed matter and high-energy physics by providing appropriate microscopic models to investigate properties of various naturally occurring physical phenomena. Thanks to recent

experimental developments, studies of dynamics in these models have emerged as an active field of research. Explorations of excited eigenstates of LGT Hamiltonians, where the gauge field is realized as quantum links, reveal a class of states having

anomalously low bipartite entanglement and anomalous values of local correlations from the thermal band. Presence of such states could have important consequences for the approach to equilibrium in isolated quantum systems, such as the existence of

long pre-thermal regimes. In this talk, we discuss various features of these quantum many-body scars (QMBS), as they are called, for both ladder and rectangular systems with infinite extent in one spatial direction.

Abstract: In this talk, I shall focus on the stroboscopic dynamics of corner modes of a second-order topological material modeled by a tight-binding free fermion Hamiltonian on a cubic lattice in the intermediate drive frequency regime for a discrete (square pulse) periodic drive protocol. I shall analyze the Floquet phases of this system and show that its quasienergy spectrum becomes almost gapless in the large drive amplitude regime at special drive frequencies. Away from these frequencies, the gapped quasienergy spectrum supports weakly dispersing Floquet corner modes. Near them, these corner modes penetrate into the bulk and eventually become indistinguishable from the bulk modes. An analytic, albeit perturbative, expression for the Floquet Hamiltonian using Floquet perturbation theory (FPT) will be provided, which will help to explain this phenomenon and lead to analytic expressions of these special frequencies. We will also see that in the large drive amplitude regime, the zero energy corner modes corresponding to the static tight binding Hamiltonian display

qualitatively different dynamics at these special frequencies.

Ref.: arXiv:2202.07671v2

Abstract: The effect of spin-orbit coupling (SoC) on quantum systems has been widely studied both in and out of equilibrium and gives rise to a diverse range of phenomena from topological insulators to spin selectivity. For quantum dot-lead systems, represented by the single impurity Anderson model, equilibrium investigations of SoC in the leads show that the combined effect of SoC and interactions on the Kondo effect is very interesting, and can even lead to a quantum phase transition of the Kondo destruction type. Our interest is to explore the possibility of similar phenomena in the steady-state of an open quantum dot-leads system, subjected to a dc bias. We begin by showing that our method of choice, the second-order Keldysh perturbation theory (PT2), benchmarks well against numerically exact methods like the TEBD, in the weak to intermediate coupling regime. Our results confirm that the linear response regime is determined by a single equilibrium scale, namely $Z\Delta$, where $Z$ is the quasiparticle fraction, and $\Delta$ is the dot-leads hybridization scale. The differential conductance in the non-linear response regime exhibits interesting trends as a function of SoC and interaction strength. We will present some of our results regarding these trends.

Abstract: Fluctuation dominated phase ordering (FDPO) refers to an unusual phase that simultaneously exhibits macroscopic order and large fluctuations. Recently it was proposed that a suitably defined local correlation can capture the macroscopic nature of such phases. We shall discuss the steady state and coarsening properties of this quantity in the coarse-grained depth (CD) models that are known to exhibit FDPO. We shall also outline the nontrivial finite size and finite time features of the 'largest' domains that dominate the ordering kinetics in these models.

Abstract: We study the stationary state of an active Brownian particle (ABP) moving in a viscous medium, in the presence of an isotropic harmonic trap in two spatial dimensions. Explicit mathematical expressions are derived for various stationary quantities of interest, using symmetry arguments and controlled approximation procedures. The probability distribution for the position of the particle shows probability distributions for the particle's position. We identify the transition from "passive" to "active" regimes, with the increase of the trap stiffness. These theoretical results are in good agreement with our numerical simulations. Numerically, we find the angular distribution for a better understanding of the orientational picture of active particles.

Abstract: In this talk, I will discuss the dynamics of an inertial active Ornstein-Uhlenbeck particle in a magnetic field. I will especially focus on how the inertia influences the dynamical behaviour of such an active particle under the action of a magnetic field, when it is confined in a harmonic trap as well as when it is set free from the trap.

Abstract: Biological systems are soft matter systems. One of the challenges in cell-biology is to understand the contribution of biomembrane processes to the cell's function. In the cell, new membrane compartments are formed during endocytosis, exocytosis, trafficking, intra-cellular division of organelles and cell-division. I will present recent advances in the biomembrane research underlying the picture of fats, lipids, and membranes. It is possible to create cell-size, membrane compartments namely Giant Unilamellar Vesicles (GUVs) with well-controlled compositions of lipids, reconstituted active transmembrane proteins and cytoskeleton at physiological buffer and temperature conditions. By fine-tuning the membrane curvature, the formation of membrane buds, membrane nanotubes as well as controlled vesicle division of membrane compartments with closed membrane necks are observed. The role of lipid membranes in the processes that are important for life such as active ions-transport, shape transformations (budding, tubulation), lateral organization of proteins, division of a membrane compartment is discussed. The potential impact of this research work falls into various areas of cell-biology, medicine, biotechnology and pharmacology.

References

• Superelasticity of Plasma‐and Synthetic Membranes Resulting from Coupling of Membrane Asymmetry, Curvature, and Lipid Sorting
  J Steinkühler, P Fonda, T Bhatia, Z Zhao, FSC Leomil, R Lipowsky, R Dimova
  Advanced Science 8, 2102109

• Tubules, beads, discs and junctions – Morphologies and dynamics of dispersed multilamellar lipid phases in excess water. T Bhatia. Journal of Colloid and Interface Science 584, 706-713

• Membrane permeability to water measured by microfluidic trapping of giant vesicles. T Bhatia, T Robinson, R Dimova. Soft Matter 16, 7359-7369

• Controlled division of cell-sized vesicles by low densities of membrane-bound proteins. J Steinkühler, R L Knorr, Z Zhao, T Bhatia, S M Bartelt, S Wegner, R Dimova, R Lipowsky. Nature communications 11 (1), 1-11

• Simple sugars shape giant vesicles into multispheres with many membrane necks. T Bhatia, S Christ, J Steinkühler, R Dimova, R Lipowsky. Soft Matter 16 (5), 1246-1258

• To Image the Orientation and Spatial Distribution of Reconstituted Na+,K+-ATPase in Model Lipid Membranes. T Bhatia, F Cornelius. Biomimetic Lipid Membranes: Fundamentals, Applications, and Commercialization

• Vesicle fluctuation analysis. J H Ipsen, A G Hansen, T Bhatia. The Giant Vesicle Book

• Capturing suboptical dynamic structures in lipid bilayer patches formed from free-standing giant unilamellar vesicles. T Bhatia, F Cornelius, J H Ipsen. Nature Protocols 12 (8), 1563

Abstract: Here, we study tracer particle motion through an entangled network of identical polymeric strands, each strand composed of two kinds of beads in a given ratio with different characteristic interaction parameters. The beads with stronger mutual interaction is called H-beads and the other set is designated as P-beads. The entangled mass is taken within an asymmetric confinement where a wall favourably interacts with one type of bead, H-wall favouring the H-beads and P-wall favouring the P-beads. The tracer particles are taken to interact more favourably with P-beads and the P-wall than the H-beads and H-wall, respectively . We study the permeation of the tracer particles from the H-wall end to reach the P-wall end through the network in presence of a driving force using the Langevin dynamics simulations. The efficiency of the network to stop the tracer particles is given by 100%-P where P is integrated density of the tracer density profile near the P-wall. We find that the efficiency decreases linearly with driving force for tracer particles below a critical size, given by the mean pore size of the network. We also observe that the permeability of tracer particles follows an Arrhenius dependence on temperature, suggesting an activated process. Our finding may help to understand the factors to control efficiency of a mask to stop respiratory droplets.

Abstract: Hard-interacting particles, commonly known as hard-sphere systems, crystallize to maximize configurational entropy above a critical density. Their equilibrium phase behaviors are governed by density as well. However, as the particle shapes become more asymmetric, the ordering of the constituent particles turns complex and intriguing. The asymmetry in shape introduces coupling between translational and orientational dynamics since the particles get interdigitated at densities close to crystallization. In this talk, I will discuss the crystallization dynamics in a two-dimensional system of Brownian squares, which exhibits distinctly different ordering upon crystallization under varied osmotic pressures. By analyzing the translational and orientational dynamics at the particle level and estimating their contribution in minimizing the free energy, I will illustrate that it is the orientational fluctuations of the particles that govern the direction along which the system equilibrates and thus the route to the final crystalline ordering. The density or the translational dynamics do not play a significant role in the process.